Mathematical Research Letters

Volume 22 (2015)

Number 6

Contact 5-manifolds admitting open books with exotic pages

Pages: 1589 – 1599



Selman Akbulut (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)

Kouichi Yasui (Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Japan)


We construct a contact 5-manifold supported by infinitely many distinct open books with the identity monodromy and pairwise exotic Stein pages (i.e. pages are pairwise homeomorphic but non-diffeomorphic Stein fillings of a fixed contact 3-manifold), moreover we describe a process of generating infinitely many such examples. In contrast to this result, on each of $\#_n S^2 \times S^3$ and $\#_n S^2 \tilde{\times} S^3 (n \geq 2)$ we construct infinitely many open books with pairwise exotic Stein pages (and identity monodromy) supporting mutually distinct contact structures.

Accepted 19 July 2015

Published 23 May 2016